[SOLVED] ECON772 Homework 3 -Testing and Dummy Variables

Testing and Dummy Variables

• Let

y = X¯ + Z° + u;

and consider the restriction

° = 0:

Show that the Wald statistic and the Likelihood Ratio statistic are the same.

• Consider the model

y = X¯ + u

where u » N ¡0;¾²I¢. Consider testing the null hypothesis,

H₀ : g (¯) = 0 vs H_A : g (¯) 6= 0

where g(¢) is a nonlinear function of g¯(.¯);

1. Find a consistent estimator of
2. Find the asymptotic distribution of your estimator; and
3. Use it to construct a Wald test statistic.

• Consider the models logW_i = ¯₀ + ¯₁Educ_i + ¯₂Female_i + ¯₃Black_i + ¯₄Asian_i + u_1i; logW_i = ®₀ + ®₁Educ_i + ®₂Male_i + ®₃White_i + ®₄Asian_i + u_2i: a) Write each ® term as a linear function of the ¯ terms,

;

.

1. Show that

¯

where ® and        are OLS estimates.

1. Show that theb b              for both equations are identically the same.